William M. Briggs

Statistician to the Stars!

Page 395 of 414

CRITICAL ASSESSMENT OF CLIMATE CHANGE PREDICTIONS FROM A SCIENTIFIC PERSPECTIVE

Here is the link to the symposium which I mentioned a few weeks back. It is being sponsored by the Ram?n Areces Foundation and the Royal Academy of Sciences of Spain, and will be held in Madrid on the 2nd and 3rd of April. Part of the introduction says:

The Royal Academy of Sciences of Spain and the Ram?n Areces Foundation wish to contribute to the creation of an informed public opinion on global change in the country. To this end, they are organising a two-day symposium aimed at scientists from different fields, decision makers and general public. Existing facts and analysis tools will be discussed, and the robustness and uncertainties of predictions made on the basis of the former, critically assessed. The meeting will provide a scientific view of existing knowledge on climate change and its expected consequences. Existing physical, chemical and mathematical tools will be discussed and climate effects will be analysed together with other concurrent changes, which tend to be overlooked in the climate change scenarios.

Presentations by the different contributors will emphasise existing scientific evidence as well as the strengths and weaknesses of predictions made on the basis of available data and modelling tools. Contributors are encouraged to express their opinions on the most relevant problems concerning the topics they will present, including scientific issues, main threats and possible mitigation or adaptation strategies.

The program is now online. My talk is entitled “Robustness and uncertainties of climate change predictions”. The deadline for me to turn it in is today. I am still working on it and not at all satisfied that I have done a good job with my topic. I am simultaneously writing a paper and the talk, and I will post both of them here, not un-coincidentally, on 1 April.

The gist of my talk I have summarized:

Global warming is not important by itself: it becomes significant only when its effects are consequential to humans. The distinction between questions like “Will it warm?” and “What will happen if it warms” is under-appreciated or conflated. For example, when asking how likely are the results of a study of global warming’s effects, we are apt to confuse the likelihood of global warming as a phenomenon with what might happening because of global warming. When of course the two kinds of questions and likelihoods are entirely separate.

Because of the frequency of confusion, I want to follow the path to the conclusion of one particular study whose results state A = “There will be More kidney and liver disease, ambulance trips, etc. because of global warming.” I start from first principles, and untangle and carefully focus on the chain of causation leading up this central claims, and quantify the uncertainty of the steps along the way.

In short, I will estimate the probability that AGW is real, the probability that some claim of global warming’s effects is true given global warming is true, and the unconditional probability that the effect is true. That’s not too much to tackle, is it?

Thank God there will be simultaneous translation of the conference, because my Spanish is getting worse and worse the more I think about it. If I was going to play soccer, then I’d be on more familiar ground. I do know how to ask that a ball be passed to me because I am alone an unguarded, and how to offer constructive criticism to a fellow teammate for not recognizing this fact and for taking a ridiculous shot at goal himself. But I am not sure how this language would apply to global warming.

Maybe your parents were right

They dropped the charges against that poor eighth-grade kid who was caught with a dollar bag of Skittles somewhere up in Connecticut. I’m not so sure that this is a good thing.

I used to eat Skittles by the pound, always saving the red and purple ones till last. My parents always warned me to drop the habit else my teeth would rot out. I didn’t listen and to the delight of my dentist and not surprisingly, they were right. I can’t eat Skittles as an entire meal anymore either. I outgrew them.

What else might your parents have been right about? They certainly warned you about your candy and if they were doing their duty, they educated you about your awful music, too. But they couldn’t have been right about that, could they? After all, your grandparents, and even their parents, said the same thing: modern music stinks. Because everybody is always saying it, you reason, it can’t be true.

Where did you get that idea?

Look at this picture. It shows a graph of music quality through time, sinking, slowly sinking, probably hitting bottom sometime in the next ten years or so. I’m at point number 4, which is the date I first heard myself echo my father when I shouted “Turn that crap down!”. My kids are at a point just off the graph, which I project is some time four to six years in the future, right before the apocalypse. My parents are at 3, the time when my blasting AC/DC on the Cougar’s eight-track machine pierced the old man’s eardrums. My grandparents came in at 2, despairing over their kid’s doo wop. Point 1 is too far back in the past for anybody to even remember.

By “music quality” I mean the obvious. You can also view this curve as something like the inverse probability that when you are in public you hear dreck pumped through speakers. This picture does not preclude that, at any time, top quality music can be found, because it obviously can be. However, the old rule that the lower the IQ the higher the volume is in force. If this graph is accurate, then I was right to switch off my kids music, and my parents were right to switch off mine. And so on. It turns out that what our ancestors were always telling us was true after all.

Music quality through time

It is nearly impossible to go anywhere today and not hear bad music. A steady stream of simplistic sound surrounds us. Every mall, restaurant, retail store, bookstore, elevator, bar, park, beach, bench, office, subway, car, bus, every damn place and every damn occasion. I fairly long to go out to eat or for a drink and enjoy nothing but silence and the murmur of conversation!

Just as you can’t eat Skittles and nothing else without rotting your teeth, you cannot listen solely to juvenile music without rotting your mind. You will positively stunt your growth injecting empty calories into your belly or empty notes into your brain.

Now, it’s good pointing out to me that Song A or Song B were excellent and that I’m a fool for not acknowledging this. Despite the fact that conversations about the niceties of juvenile music often bear an eerie similarity to, and have all the intellectual content of, in-depth discussions over the indiscernible differences between Diet Coke and Diet Pepsi, I won’t disagree with you that Song A is just the thing. Sometimes. Occasionally. But not everyday and not every time you have to shop for toilet paper.

Please just shut it off.

Another reason to leave academia

1. Repeat after me: “There are no innate biological differences between men and women…except, well, women are of course better nurturers, sympathizers, empathizers, and a score of other things.”

2. Now use the law (Title IX) designed to enforce equal numbers of girls playing sports as boys to mandate an even number of women and men in physics and math departments in universities that receive federal funding (which is all universities except one or two).

3. Then try applying for a grant with a male as PI.

Full story here
. With full props to Arts & Letters Daily.

Some hilarity from the article:

For one thing, the Title IX compliance reviews are already underway. In the spring of 2007, the Department of Education evaluated the Columbia University physics department. Cosmology professor Amber Miller, talking to Science magazine, described the process as a ?waste of time.? She was required to make an inventory of all the equipment in the lab and indicate whether women were allowed to use various items. ?I wanted to say, leave me alone, and let me get my work done.? But Miller and her fellow scientists are not going to be left alone.

“Say, are women allowed to use this slide rule?”

All this is fair enough, of course, because as we certainly must believe, “There are no innate biological…”. As for me, I cannot wait, if this law is passed, for the comedic opportunities when the first male sues a woman’s studies department, or English, or etc., to force them to hire more men. And naturally, lawyers will be brought in to judge the merit of promotions. Who better than a lawyer to judge differences in papers on string theory?

It depends what the meaning of mean means.

Yesterday’s post was entitled, “You cannot measure a mean”, which is both true and false depending—thanks to Bill Clinton for the never-ending stream of satire—on what the meaning of mean means.

The plot I used was a numerical average at each point. This implies that at each year there were several direct measures that were averaged together and then plotted. This numerical average is called, among other things, a mean.

In this sense of the word, a mean is obviously observable, and so yesterday’s title was false. You can see a mean, they do exist in the world, they are just (possibly weighted) functions of other observable data. We can obviously make predictions of average values, too.

However, there is another sense of the word mean that is used as a technical concept in statistics, and an unfortunate sense, one that leads to confusion. I was hoping some people would call me on this, and some of you did, which makes me very proud.

The technical sense of mean is as an expected value, which is a probabilistic concept, and is itself another poorly chosen term, for you often never expect, and cannot even see, an expected value. A stock example is a throw of a die, which has an expected value of 3.5.

Yesterday’s model B was this

B: y = a + b*t + OS

I now have to explain what I passed over yesterday, the OS. Recall that OS stood for “Other Stuff”; it consisted of mystery numbers we had to add to the straight line so that model B reproduced the observed data. We never know what OS is in advance, so we call it random. Since we quantify our uncertainty in the unknown using probability, we assign a probability distribution to OS.

For lots of reasons (not all of them creditable), the distribution is nearly always a normal (the bell-shaped curve), which itself has two unobservable parameters, typically labeled μ and σ^2. We set μ=0 and guess σ^2. Doing this implies—via some simple math which I’ll skip—that the unknown observed data is itself described by a normal distribution, with two parameters μ = a + b*t and the same σ^2 that OS has.

Unfortunately, that μ parameter is often called “the mean“. It is, however, just a parameter, an unobservable index used for the normal distribution. As I stressed yesterday (as I always stress), this “mean” cannot be seen or measured or experienced. It is a mathematical crutch used to help in the real work of explaining what we really want to know: how to quantify our uncertainty in the observables.

You cannot forecast this “mean” either, and you don’t need any math to prove this. The parameter μ is just some fixed number, after all, so any “forecast” for it would just say what that value is. Like I said yesterday, even if you knew the exact value of μ you still do not know the value of future observables, because OS is always unknown (or random).

We usually do not know the value of μ exactly. It is unknown—and here we depart the world of classical statistics where statements like I am about to make are taboo—or “random”, so we have to quantify our uncertainty in its value, which we do using a probability distribution. We take some data and modify this probability distribution to sharpen our knowledge of μ. We then present this sharpened information and consider ourselves done (these were the blue dashed lines on the plot yesterday).

The unfortunate thing is that the bulk of statistics was developed to make more and more precise statements about μ : how to avoid bias in its measurement, what happens (actually, what never can happen) when we take an infinite amount of data, how estimates of it are ruled by the central limit theorem, and on and on. All good, quality mathematics, but mostly besides the point. Why? Again, because even if we knew the value of μ we still do not know the value of future observables. And because people tend to confuse their certainty in μ with their certainty in the observables, which as we saw yesterday, usually leads to vast overconfidence.

From now on, I will not make the mistake of calling a parameter a “mean”, and you won’t either.

Harmonica Convergence: classic column

In 1987 in Sedona, Arizona, the end of the world occurred in an event called the “Second Harmonic Convergence“. It was publicized all over the world. Many enlightened people came. Not everybody got the right idea.


The Second Harmonica Convergence, by Lem Polomski


I had missed the first Harmonica Convergence as I was touring Lichtenstein with the Borscht Five Polka band, which as you might remember was started by three ex-members of the Traveling Schmenges. So you can imagine my excitement when I discovered that I would be on tour in Arizona for the famed event. I took a diversion and arrived early. I worked feverishly the night before, polishing my best Steinowski—a forty-six holer. I would be ready. At five the next day, many hundreds were milling around on the Mesa, many still in their bathrobes. When would we play! I kept my beloved instrument under wraps as no one else had their harmonica out. Finally everyone joined hands in a large circle. They began humming. Concert C! This was it! They were about to tune up. I could stand no more and pulled out my brass beauty and began an impassioned rendition of the “She’s Too Fat For Me” Polka. I would show these Americans a true Harmonica Convergence! Imagine my confusion when no one joined in. Instead several of the bathrobed convergers chased after me with large crystalline rocks, chanting in a strange language. I left, dejected, and washed away my troubles with some tasty cabbage rolls and coffee and am now a wiser, more spiritually fulfilled person.

« Older posts Newer posts »

© 2014 William M. Briggs

Theme by Anders NorenUp ↑